ELIZABETH BISHOP'S steadily widening audience and her endurance among the readers she has once claimed are the reward of constancy to an ideal object. Her reputation is founded on perhaps 25 poems, among them ''Love Lies Sleeping,'' ''The Unbeliever,'' ''The Shampoo,'' ''Over 2,000 Illustrations and a Complete Concordance,'' ''Arrival at Santos'' and ''First Death in Nova Scotia.'' Altogether that looks like a modest achievement until one considers that most of the larger poetic reputations of the past century have been founded on similar evidence. The difference is that Bishop's masterpieces stand in a higher ratio to her work as a whole. She published little, because she would not release a poem that fell short of a complete conception; and what strikes one most in reading her poems again is the way they answer each other across pages or volumes, so that each plays its part: ''The Bight,'' for example, earning our esteem for the sake of its much fuller picture of the dream house sketched in ''The End of March''; the figure of streets coupled to stars, a mystery in ''Going to the Bakery,'' somehow clarifying a similar figure in ''Love Lies Sleeping.''

This ''Complete Poems'' is actually the second book Farrar Straus & Giroux has published under that title. In 1969 Bishop herself supervised the publication of the earlier ''Complete Poems,'' including all of ''North & South'' (1946), ''A Cold Spring'' (1955) and ''Questions of Travel'' (1965), with some translations and uncollected poems. This new edition adds all of ''Geography III'' (1976), a few more translations, four uncollected poems from Bishop's last years and five more written between 1939 and 1962. The earliest of these five, ''Pleasure Seas,'' is a genuine discovery: a poem accepted for publication but never printed, which might have appeared without embarrassment in ''North & South''; in style it is something between ''Florida'' and ''The Imaginary Iceberg,'' though the poem it most nearly recalls is Wallace Stevens' ''Sea Surface Full of Clouds.''

So far the editorial choices are straightforward and comfortable; yet the new ''Complete Poems'' contains two further sections: ''Poems Written in Youth'' and ''Occasional Poems.'' Among the ''Poems Written in Youth'' one may discover, together with many schoolmagazine items, the sequence of ''Three Valentines'' praised by Marianne Moore, which shows Bishop's congeniality with the idioms of 17th-century verse and falls just within the limits of pastiche. But it is the ''Occasional Poems'' that readers are likely to find unsettling. The lofty heading covers nothing but some scraps - ''Lullaby for the Cat,'' ''Lines Written in the Fannie Farmer Cookbook'' - intimate and trivial verses meant for friends, none of which would have pleased Bishop, who did not believe in scraps.

''Elizabeth Bishop and Her Art,'' edited by Lloyd Schwartz and Sybil P. Estess, is a packed receptacle of miscellaneous documents: reviews of her books, interviews with and about the poet, blurbs she wrote for other people's books and blurbs they wrote for hers, speeches with which fellow poets introduced her at public readings, several essays, and memorials by several hands, including two by a single admirer, who presents her in prose as ''a living doll'' and in verse as ''a Dream Boat.'' Teachers as well as gossips will find this book intermittently useful. The most intelligent comments in the anthology come from two poets who speak as if they had never met Elizabeth Bishop. Octavio Paz observes that her poetry has ''the lightness of a game and the gravity of a decision.'' John Ashbery says of her supposed debt to Moore, ''the two poets couldn't be more different; Miss Moore's synthesizing, collector's approach is far from Miss Bishop's linear, exploring one.'' The truth is that Moore served as a kind of unofficial sponsor for Bishop in her early years, and the confusion seems to have started then.

It was not entirely a confusion. Moore's influence on Bishop was real though narrow, like the influence of Edward Arlington Robinson on Robert Frost. An original-minded author can profit incalculably from this sort of dependence: the respect one feels for the master of an earlier generation who has shown an unshakable interest in one's own fate. The result in Bishop's case was more than elective affinity and less than discipleship. Of the poems in ''North & South,'' only ''Casabianca'' is a simple imitation; ''The Man-Moth'' presumes an audience trained by Moore; ''Wading at Wellfleet'' uses her discipline with traces of her diction, but the sustained metaphor of the sea as chariot gives the closing lines a power that belongs uniquely to Bishop's fable: This morning's glitterings reveal the sea is ''all a case of knives." Lying so close, they catch the sun, the spokes directed at the shin. The chariot front is blue and great. The war rests wholly with the waves: they try revolving, but the wheels give way; they will not bear the weight. So too with a later poem like ''Visits to St. Elizabeths.'' One can imagine Moore conceiving a house-that-Jack-built structure for a poem about Erza Pound's incarceration in a mental hospital after a verdict of insanity saved him from being prosecuted for treason. Yet no one but Bishop could have found the wit and courage to begin flatly, ''This is the house of Bedlam./ This is the man / that lies in the house of Bedlam,'' or to characterize Pound himself by a succession of adjectives for ''man'' that gather force as the house is built. We hear of him first as ''the tragic man'' in the cant of the day, then as ''the honored man,'' then ''old'' and ''brave'' and ''cranky''; and at last ''cruel,'' ''busy,'' ''tedious,'' ''wretched'' -until we look in on him from the moral world outside, the world against which a great deal of modern poetry like Pound's had contrived so careful a shelter.